The present invention relates generally to a transversal filter and particularly to a transversal filter used for processing of a digital audio signal.
The processing of a digital audio signal modulated by a pulse-code modulation system, hereinafter referred to simply as a PCM system, is usually accomplished by controlling the frequency characteristic of the PCM signal which is sampled at a constant sampling frequency. To achieve such control, an infinite impulse response (hereinafter referred to as "IIR") digital filter and a finite impulse response (hereinafter referred to as "FIR") digital filter are generally used. The IIR digital filter has the advantage that design formule in closed form can be used to design an IIR filter in which variable frequencies can be selected. However, such a design neglects the phase characteristic of the filter. Therefore, it is difficult for an IIR digital filter to obtain both a desired amplitude characteristic and a desired phase frequency characteristic.
On the other hand, if a transversal filter utilizing a set of FIR filters is to be designed with desired frequency characteristic over a frequency bandwidth extending from low frequency to a frequency near f.sub.s /2, where f.sub.s is a sampling frequency, an unacceptably high order of filter design is required. As a result, the transversal filter has the disadvantage of being too complex in comparison with the IIR digital filter. To eliminate this disadvantage, it has been proposed to divide the frequency band into some frequency bands below f.sub.s /2. The transversal filters are then used for the frequency bands. A predetermined frequency characteristic is then obtained by synthesizing the filtering frequency characteristics of the respective filters, thereby reducing the complexity of the apparatus. However, it becomes difficult to design the crossover frequency characteristic in each frequency band because in the low frequency band, in addition to the sampling at the sampling frequency f.sub.s, a subsampling is also effected at a subsampling frequency f.sub.s ', which is lower than the sampling frequency f.sub.s. Further, it is also difficult to design the filter's order if a filter having an arbitrary frequency characteristic is to be obtained.